1. A simple probability question

The probability of happening the event A is 0.7 and that of event B is 0.5. If the events are independent, what is the probability of of happening

a) either of them
b) none of them

I know its simple..but I am stuck

Thanks

2. Re: A simple probability question

Just write the definition of independence. What is it?

3. Re: A simple probability question

Ans for qn. b). is 0.01.

But have doubt with qn. a) ..I think it is P (A or B) . not P (A and B).
so the ans is 1- 0.01 = .99.
is this correct?

4. Re: A simple probability question

I also think that it's $P(A\cup B)$.. But I don't understand why you find 0.01 for $P(A^c\cap B^c)$.

5. Re: A simple probability question

a) Since the events are not mutually exclusive, P (A or B)= P(A) + P (B) - P (AUB) = 0.7+ 0.5 - 0.35=0.85

b) 1-0.85 = 0.15

Please discard the previous ans. instead of 0.7 i used 0.8 for P(A). Now I hope I am correct. am I?

6. Re: A simple probability question

P(A union B)=P(A)+P(B)-P(A intersection B) (see Probability of a union here)
but A and B are independent implies P(A intersection B)=P(A)*P(B)
As a consequence:
P(either happens)=P(A union B)=P(A)+P(B)-P(A intersection B)=P(A)+P(B)-P(A)*P(B)=0.7+0.5-0.7*0.5=0.85
and
P(none happens)=1-P(either happens)=1-0.85=0.15

7. Re: A simple probability question

Yes, except that in the formular for P(A or B) it's $P(A\cap B)$, not $P(A\cup B)$.

8. Re: A simple probability question

thanks for both of you